Internal variables in thermoelasticity

• Main Author: Berezovski, Arkadi
• Other Authors: Ván, Peter
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer, 2017.
• Series: Solid mechanics and its applications ; v. 243.
• Subjects: Thermoelasticity.; elektronické knihy; electronic books
• ISBN: 9783319569345; 9783319569338
• Physical Description: 1 online resource (222 pages)

This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material's reaction to...

Table of Contents:

• Preface; Contents; 1 Instead of Introduction; 1.1 One-Dimensional Elastic Waves in Heterogeneous Solids; 1.1.1 Single Inclusion; 1.1.2 Periodic Laminate; 1.1.3 Functionally Graded Material; 1.1.4 Remarks; 1.2 Models for One-Dimensional Dispersive Waves in Solids with Microstructure; 1.2.1 Classical Wave Equation; 1.2.2 Strain Gradient Model; 1.2.3 Linear Version of the Boussinesq Equation; 1.2.4 Love-Rayleigh Equation for Rods Accounting for Lateral Inertia; 1.2.5 Refined Models; 1.2.6 Models with Higher-Order Time Derivatives; 1.2.7 Remarks; 1.3 Conclusions; References.
• Part I Internal Variables in Thermomechanics2 Introduction; 2.1 Micro versus Macro; 2.2 Internal Variables and Dynamic Degrees of Freedom; 2.2.1 Internal Variables of State; 2.2.2 Internal Dynamic Degrees of Freedom; 2.2.3 Similarity and Differences; 2.3 Generalization: Dual Internal Variables; 2.4 Historical Remarks; References; 3 Thermomechanical Single Internal Variable Theory; 3.1 Introduction; 3.2 Thermodynamic Rheology; 3.2.1 Balance Laws; 3.2.2 The Second Law of Thermodynamics; 3.2.3 Linear Solution of Dissipation Inequality for Isotropic Materials.
• 3.2.4 Elimination of the Internal Variable3.2.5 Rheology and Thermodynamics; 3.3 Material Thermomechanics; 3.3.1 Material and Spatial Time Derivatives; 3.3.2 Balance Laws; 3.3.3 Material Form of the Energy Conservation; 3.3.4 Material (Canonical) Momentum Conservation; 3.4 Single Internal Variable Theory; 3.4.1 Dissipation Inequality; 3.4.2 Simple Evolution Equation for Internal Variable; 3.5 Example: Phase Field Theory; 3.6 Conclusions; References; 4 Dual Internal Variables; 4.1 Introduction; 4.2 Dual Internal Variables; 4.2.1 Non-zero Extra Entropy Flux.
• 4.2.2 Evolution Equations for Internal Variables4.2.3 Fully Dissipative Case; 4.2.4 Non-dissipative Case; 4.3 Example: Cosserat Media; 4.3.1 Linear Micropolar Media; 4.3.2 Microrotation as an Internal Variable; 4.4 Example: Micromorphic Linear Elasticity; 4.4.1 The Mindlin Microelasticity; 4.4.2 Rearrangement; 4.4.3 Microdeformation Tensor as an Internal Variable; 4.4.4 Remark on Second Gradient Elasticity; 4.5 Conclusions; References; Part II Dispersive Elastic Waves in One Dimension; 5 Internal Variables and Microinertia; 5.1 Introduction.
• 5.2 Single Internal Variable: One-Dimensional Example5.2.1 Evolution Equation for a Single Internal Variable; 5.3 Dual Internal Variables in One Dimension; 5.3.1 Example: Linear Elasticity; 5.4 Summary and Discussion; References; 6 Dispersive Elastic Waves; 6.1 One-Dimensional Thermoelasticity in Solids with Microstructure; 6.2 Description with Single Internal Variable ; 6.3 Dispersive Wave Equation with Direct Coupling; 6.4 Dispersive Wave Equation with Gradient Coupling; 6.5 Description with Dual Internal Variables; 6.6 Microstructure Model with Direct Coupling.